# Questions about the speed of light

• Xilor
In summary, the speed of light, denoted by c, is a constant and does not change regardless of the observer's frame of reference. This means that no matter how fast an observer is moving, they will always measure the same speed of light. This is due to the principles of time dilation and length contraction, which affect the measurements of time and distance. When measuring the speed of light, an observer needs a ruler, a timer, a light source, and a mirror. They measure the distance and time it takes for the light to travel to and from the mirror, and use those measurements to calculate the speed of light. This experiment can be repeated by different observers with different rulers and timers, and they will all get the same value

#### Xilor

Hi, I hear that light always seems to travel at c, but I've failed to completely understand what that means, could anyone help out with that?

c is measured in m/s, but both seconds and meters seem to be able to change depending on the observer due to time dilation and length contraction. When talking about m/s are we talking about Earth seconds, or the observers seconds? And are we talking about Earth meters, observers meters, universal meters or light meters?

Is the constant speed only about how quickly the observer sees light arrive or pass by, or is it also about how an observer would experience light traveling along the entire path? If a observer traveling at 99.9999% the speed of light along the same path would measure the light arriving, which variables would be the same as compared to an observer which is static? Which would be different if any?

I thought that this experiment could help me make more sense of it all: Place two lightsources right next to each other, both at a distance of 299792458 meters away from the points where some equipment will be. Both the lightsources and the points are the same distance apart of each other. All clocks mentioned were synchronized to a time at the start, and have been moved in such a way that no dillations have occurred that would cause them to lose their sync.

Both lightsources fire off a pulse towards their respective points, both in the same direction, which is done at T0.
Put a static observer at one of the points, this static observer receives the light signal and notes the time T1.
Take a second observer moving at half the speed of light, starting at 149896229 meters away from the same point from the same direction as the light came from, which is also being released at t0. When the light hits this observer, it notes T2 on its own clock, but also sends a quick light pulse to a stationary clock right next to it (assume distance = 0, or very close to it) , which notes T3 as soon as this lightpulse hits.
What can now be said about any of these times? Is T1 - T0 a second? Is T1 the same as T2? Is T1 the same as T3? Would both of the observers see the light arriving at 299792458 m/s? Are there any other interesting things that could be said about the results, or any more interesting results that could be found if the experiment was tweaked somehow?

Xilor said:
Hi, I hear that light always seems to travel at c, but I've failed to completely understand what that means, could anyone help out with that?

c is measured in m/s, but both seconds and meters seem to be able to change depending on the observer due to time dilation and length contraction. When talking about m/s are we talking about Earth seconds, or the observers seconds? And are we talking about Earth meters, observers meters, universal meters or light meters?
When an observer measures the speed of light, he needs four things: a rigid ruler of any arbitrary length, a stable timing device ticking at any arbitrary rate, a light source that can be turned on and off, and a mirror. He places the mirror some distance away from the light source and he measures that distance with his ruler. He goes back to the light source, quickly turns it on and off and starts his timer. The observer cannot see or observe or have any awareness of the progress of the light pulse as it travels toward the mirror or as it hits the mirror or as it travels back toward the observer until it finally hits the observer's eyes and he stops the timer. He can now calculate the speed of light as being twice the measured distance divided by the measured time interval.

Every time he repeats this experiment, even when he is traveling at a high speed with respect to his first measurement, he always gets the same answer. But recognize that the mirror and timer have to be traveling with the observer, although the light source does not have to be, as long as he can start his timer when the light reaches him and that it travels on toward the mirror and reflects back to him.

Furthermore, if someone else repeats the measurement with a different length ruler and a timer running at a different rate, they can bring their rulers and timers together and compare them and see that they both got the same value for the speed of light.
Xilor said:
Is the constant speed only about how quickly the observer sees light arrive or pass by, or is it also about how an observer would experience light traveling along the entire path? If a observer traveling at 99.9999% the speed of light along the same path would measure the light arriving, which variables would be the same as compared to an observer which is static? Which would be different if any?
Hopefully, my previous comments will allow you to answer all these questions.
Xilor said:
I thought that this experiment could help me make more sense of it all: Place two lightsources right next to each other, both at a distance of 299792458 meters away from the points where some equipment will be. Both the lightsources and the points are the same distance apart of each other. All clocks mentioned were synchronized to a time at the start, and have been moved in such a way that no dillations have occurred that would cause them to lose their sync.
You cannot synchronize clocks and then move them and expect them to remain synchronized. You have to move them and then synchronize them by sending light signals between them using a process that I'll explain later.
Xilor said:
Both lightsources fire off a pulse towards their respective points, both in the same direction, which is done at T0.
Put a static observer at one of the points, this static observer receives the light signal and notes the time T1.
Take a second observer moving at half the speed of light, starting at 149896229 meters away from the same point from the same direction as the light came from, which is also being released at t0. When the light hits this observer, it notes T2 on its own clock, but also sends a quick light pulse to a stationary clock right next to it (assume distance = 0, or very close to it) , which notes T3 as soon as this lightpulse hits.
What can now be said about any of these times? Is T1 - T0 a second?
You have just described the process of synchronizing clocks so of course the answer is yes, but only because you have set the time on the remote clock so the answer will come out to be one second.
Xilor said:
Is T1 the same as T2?
Since T2 is on a moving clock, it is not possible to answer this question until we know where it was at time zero.
Xilor said:
Is T1 the same as T3?
Yes.
Xilor said:
Would both of the observers see the light arriving at 299792458 m/s?
Yes, as long as they use their own mirrors, rulers and timers.
Xilor said:
Are there any other interesting things that could be said about the results, or any more interesting results that could be found if the experiment was tweaked somehow?

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Hmm, I see, thank you.

So, if I understood you correctly the static speed of light is true along the entire path of the light, it's just impossible to actually observe it. And no matter what kind of experiment could be devised, the speed of light would always seem to both arrive and seem to have traveled all the way at c? And that any measurements that could be taken would always end up the same even if the length of seconds change for an observer as meters change for that observer at the same ratio?

You're getting close. We cannot determine that light propagates along a path at c, but we can measure that its progress is a constant speed, independent of the motion of the source of the light. We merely assign that speed to be c when we want to make a Frame of Reference according to Einstein's convention. The rest of your statements are correct.

Hmm, how can that constant speed be measured outside the speedmeasuring device you mentioned?
If hypothetically an area of space would exist where both distances and the speed of light would be twice as high, then I can't think of anything outside that area that would be able to separate those based purely on measured speeds, is that right?
Or does that constant speed assume that all distances are equal? Isn't it possible for spacetime to get warped to have longer distances? So that the distance (and angle) from us to a point A and B would not mean that we could calculate the exact distance between A and B.

First off, we're not talking about any warping of spacetime. In Special Relativity, spacetime is perfectly linear.

Secondly, we are talking about rather short distances that can be measured with a rigid ruler. Not only that, but the distance between the observer with his timer and the mirror must be attached to a rigid structure to exactly maintain the measured distance.

Thirdly, this speedmeasuring device only works for a round trip of the light. It gives us no clue how to divide up the times for each direction of the trip. All we know is the total time and from that we can get the "average speed".

Now I didn't go into any details on how to determine that the speed of light along a one-way path is a constant (not necessarily c) so I'll do that now. We still have to have a rigid structure with a shutter mechanism mounted some distance away from a pair of detectors. We don't care what that distance is, only that it's stable. Then we line up the apparatus along the path of two distant light sources that are moving toward or away from us a different speeds, such as a binary star. Then we open the shutter at the front of our apparatus and look to see if the light from both sources reaches the other end of our apparatus at the same time, which it will.

OK, now I'll try to address your concerns, although I will not answer each question because I hope you will be able to see that some of the questions are not relevant.

So let's say that after you measure the round trip speed of light, you claim that the light took one quarter of the total time to get to the mirror and three-quarters of the total time to get back. Now you will determine that the forward speed of the light is twice c and in the other direction coming back it is two-thirds c. You will note that the average of these two speeds is not c which is why I earlier put "average speed" in quotes.

The whole purpose of taking you through this lengthy exercise is to emphasize that we can't measure the one-way speed of light; we can't know that it is actually or really c or some other constant in any given situation. But if we claim that is one particular value in one direction, that fixes its speed in the other direction.

So when Einstein says to assign equal times to the two directions of the round-trip measurement of the speed of light, he's not getting that from nature, rather, he's making a declaration about how he's going to set up his concept of synchronized clocks as part of his definition a Frame of Reference.

Xilor said:
[..] Are there any other interesting things that could be said about the results, or any more interesting results that could be found if the experiment was tweaked somehow?